YOU WOULD be forgiven for thinking that football is an old man's game. Tom Brady, the league's best quarterback, is 38, and the best running back, Adrian Peterson, is an ancient-by-that-gig's-standards 30. Those two are joined in 30-and-up triumph by, among others, Carson Palmer, Philip Rivers, Larry Fitzgerald and Brandon Marshall. Colts QB Matt Hasselbeck, 40, won his first four starts in place of injured wunderkind Andrew Luck, who's 26.

The sport at its highest level takes years to master, but the median player is a hair over 26, and the average career spans less than seven years, according to the NFL. Just when you learn to play the game, you're drummed out of it. There are countless players who would have joined the aforementioned group if not for frizzled ligaments, broken bones or just plain getting old.

Old, old, old. Adam Vinatieri is so old.... How old is he? The Colts' kicker is so old that the offensive and defensive rookies of the year in his debut season played their last NFL games in 2004 and '07, respectively. He's so old that the kicker whose job he took in his first training camp turns 60 next July. He's so old that he played against Reggie White in Super Bowl XXXI, XIX years ago. He's so old that he once tackled Herschel Walker. He's so old that, as punter Pat McAfee said in November, "the guy is wearing Depends, and he's knocking down game-winners every week."

Vinatieri turns 43 on Dec. 28, which makes him the oldest player in the NFL, a title he's held since kicker Jason Hanson retired in 2012. In '15, Vinatieri has made 89.5% of his field goals (including three of four beyond 50)—a higher success rate than in 15 of his previous 19 seasons. In other words, he's still kicking.

This would have been a remarkable feat a decade ago, but it's far more impressive when you consider today's competition. In 2015 kickers across the league have a hit rate of 84.8%. Compare that with 1995, one year before Vinatieri broke in, when kickers hit just 77.4% of field goal attempts. A seemingly endless supply of strong-legged, dream-chasing soccer converts waits for every well-paid veteran to falter, and Vinatieri has held them all off. The kicker who competed against him in training camp last season, rookie Cody Parkey, wound up making the Pro Bowl after a trade to the Eagles. For his part, Vinatieri made the Pro Bowl too, on the strength of the league's most accurate season: 96.8%.

One year later Vinatieri is the wisest, oldest veteran on the league's oldest team. Indy, the island of well-worn misfit toys, this off-season alone added Andre Johnson (34), Trent Cole (33) and Frank Gore (32). Johnson is on pace for his worst season ever; Cole is trending for a career-low sack total; and Gore, coach Chuck Pagano says, "is beat to crap." And yet: Experience may be what it'll take to win the underwhelming AFC South.

OVER THE last two decades Vinatieri has had perhaps the most illuminating perch from which to witness the transformation of the NFL. He's played for Dungy, Belichick, Carrol and Parcells (who, he says, "made you nervous"). He's suited up alongside Brady, Manning and Luck.

On Brady versus Manning he says: "Brady's like a kid that, on the playground, just does his thing. And he's just good. Manning is the guy who's meticulous, almost OCD; I've never seen a guy prepare, study that hard. S---, he might as well be the coordinator, the GM and the coach. He may be the smartest player I've ever seen." As for Luck, Vinatieri says the QB's been a star since he started, knew the playbook from Day One, but ... "he needs to have a little more a------in him." And Vinatieri grimaces every time Luck takes a hit. "I'm thinking, No! Don't take those hits."

He wishes he remembered more. Two nights before the Patriots played the AFC championship game in Pittsburgh in 2002, Vinatieri was reminiscing with the key figures on what was about to become the NFL's next dynasty: Willie McGinest, Ty Law, Tedy Bruschi, maybe Brady—he's a little foggy on who was there. "Those are the fun times," he says, "sitting around with your buddies, talking about crazy s---that happened back in the day. No drinking, just sitting around a table, talking. It was awesome."

Here he points to a reporter's tape recorder. "Thinking back, that's always when I'm like, 'Damn—I wish I had one of these.'"

LIKE SO many other kickers, Vinatieri has a career born from contingency. At Rapid City (S.D.) Central High he kicked, yes, but he also played QB and lettered in soccer, wrestling and track. "If I could have picked, I would have been 6'4" and able to throw," he says, "but I knew kicking was my only shot." Maxed out at six feet, he landed at South Dakota State, and even that was a fallback plan.

In high school Vinatieri had applied to Army and Air Force, in large part because he'd enjoyed Top Gun. Three weeks at West Point was enough time away from home, though, and when he left, only SDSU—two hours from his hometown in Yankton—still had a roster spot for him. There he set the Jackrabbits' all-time scoring record and won two D-II championships, but SDSU isn't exactly known for shipping talent to the pros. So in 1995, after his graduation, Vinatieri—having completed premed courses, figuring that cardiac surgery was a good enough fallback if pro football didn't work out—landed on the Amsterdam Admirals in the World League of American Football.

The Patriots signed him after that spring season to compete in camp for the job of kickoff specialist. As Vinatieri remembers it, neither incumbent placekicker Matt Bahr nor punter Tom Tupa could kick off. Before New England's third preseason game, Parcells told Vinatieri he would handle not just kickoffs that night but also field goals. "He said, 'Let's see if you've got what it takes—or you're going to pack up your s---and go home.'" Vinatieri made all three of his field goals and all three of his extra points, and it was Bahr (a 17-year veteran beloved by Parcells) who had to pack up his s---and go home.

Vinatieri has always had a strong right leg, and age has hardly weakened it. But he says what distinguishes him is his ability to clear his head under pressure: "There are more talented kickers. But the thing I do fairly well is that I can focus in."

Rare is the kicker who's remembered for anything other than his mistakes. But Vinatieri belongs to the class of athletes popularly endowed with the gene called "clutch." Although he never did get around to enrolling in medical school, he's probably the Pro Bowl kicker you'd trust most with a scalpel.

There was his kick for the Pats in the Tuck Rule game against the Raiders in January 2002: After Brady's apparent fumble became an incompletion, Vinatieri still had to hit a 45-yarder in the last minute of regulation to tie things up. For that boot, on account of snow that he figured would keep Oakland's line from getting a good push, he aimed lower than usual. "I kick it, and it's like a frickin' 2-iron—15 feet off the ground. Once it cleared the line, it took forever. I could barely see the referees or the ball." The kick was good, and Vinatieri hit another to win it in overtime.

Two weeks later, in Super Bowl XXXVI, Vinatieri had to make one from three yards farther out (and with the fourth-quarter clock expiring) in order for his two-TD-underdog Patriots to upend the Rams. "As loud as it was, it felt quiet in my head, like in the movies," recalls Vinatieri. "When it left my foot, I was like, 'Oh, that felt perfect.' I think I was doing this"—Vinatieri raises his arms high above his head—"before it even hit the net."

Better to be lucky than good, it's often said, and as sports aphorisms go, it's among the easiest to defend. In the NFL in particular, volatility makes legends out of career afterthoughts. But it works just as well outside of football. Consider: During the Great Sioux War of 1876, General George Custer ordered his Seventh Cavalry to attack Indian encampments near the Little Bighorn River in Montana. These were highly decorated Civil War veterans, and they were, as we now know, set up to be slaughtered. Sitting Bull, Crazy Horse and their charges killed nearly half of the Seventh Cavalry, including Custer and two of his brothers.

Where does luck come in? Custer instructed his cavalry's band not to fight alongside him that day, leaving them instead on the supply steamboat, away from the skirmish. The band, made up primarily of European immigrants, all survived the military blunder, and their Italian leader, a Yankton settler, was discharged from service later that year. He would go on to write some of the earliest operas from the American West. His name? Felix Vinatieri.

Felix's great-great-grandson chose a line of work in which plenty of good careers have lacked luck. Adam cites Hanson, for one, who kicked for the Lions from 1992 through 2012. "He is really good—I mean, really good," says a man who should know, who's clocked in more times (302 games to date) than any active player. "But he only played in a handful of playoff games. Sheesh. What if he'd played on a different type of team? I've been lucky."

The two franchises Vinatieri has played for? They've only been the league's winningest (Patriots) and fifth winningest (Colts) during his career. Vinatieri has seen more playoff games than any player ever. More luck: After his third season, the Browns (the losingest team in that stretch) offered him a contract. Mercifully, New England matched it. Three years later, after his kick won Super Bowl XXXVI, with suitors elsewhere, the Patriots slapped their franchise tag on the kicker. He grumbled before signing a longer deal and winning two more titles with the Pats. "What if I'd gone to Cleveland for 15 years? Maybe [New England] handcuffed me a little bit, but it worked out O.K."

When finally he decided to skip town in the spring of 2006, he managed to get a strong offer from a Colts team that just couldn't get past New England in the playoffs. With Vinatieri, Indy immediately won the Super Bowl, but not before their new kicker scored every point in a 15--6 division-round win over the Ravens and then provided the decisive field goals (3 for 3) in a 38--34 AFC championship game win over his old team.

Eight years later, another AFC title game elevated the Colts-Pats rivalry: After New England blew out Indy 45--7 last January came Deflategate, the winners tarred in the press as cheaters, the losers as tattletales. "I tried to stay away from all that," says Vinatieri, who turned down TV requests as the scandal erupted. He doesn't wish the Patriots any harm. "I still give Mr. Kraft a hug every time I see him; he was like a father to me."

And what of Spygate, which clouded the early title runs? "A lot of people were talking—Do they really deserve these wins? Do they deserve blah, blah, blah? S---, man. Look at all these players and their blood, sweat and tears, all the hard work we put in. I know exactly what we sacrificed. It made me mad."

WHAT'S LEFT for Vinatieri? He's stopped thinking beyond the now, owing to the unpredictability in his recovery time. He says, "I don't feel like I've lost a lot of strength—but I can't kick every day anymore. And I'm in the training room all the time."

He's at the mercy of his own body. But he's not especially eager to do anything else. He enjoys the outdoors—Vinatieri has hunted big game everywhere from Africa to the Arctic Circle; he even spoke at a 2014 event during the NRA's annual meetings—and spending time with his wife, Valerie, and their three children. He figures he's insufficiently edgy for the job of TV analyst.

So he'll keep chasing the fifth ring, which would tie him with Charles Haley for the most won as a player, until he can't anymore. "If [we win it all] this year—shoot, would I be gone?" he asks. "I'm not making any predictions. But it would be fun to win another one, that's for damn sure." And the old man is going to make certain, this time, that he documents every second of it. That, too, is for damn sure.